inverse function

Math.the function that replaces another function when the dependent and independent variables of the first function are interchanged for an appropriate set of values of the dependent variable. In y = sin x and x = arc sin y, the inverse function of sin is arc sine.[181020]
* * *
Mathematical function that undoes the effect of another function.For example, the inverse function of the formula that converts Celsius temperature to Fahrenheit temperature is the formula that converts Fahrenheit to Celsius. Applying one formula and then the other yields the original temperature. Inverse procedures are essential to solving equations because they allow mathematical operations to be reversed (e.g. logarithms, the inverses of exponential functions, are used to solve exponential equations). Whenever a mathematical procedure is introduced, one of the most important questions is how to invert it. Thus, for example, the trigonometric functions gave rise to the inverse trigonometric functions.* * *
Universalium. 2010.
Look at other dictionaries:
inverse function — n. the function obtained by expressing the independent variable of another function in terms of the dependent variable which is then regarded as an independent variable … English World dictionary
Inverse function — In mathematics, if fnof; is a function from A to B then an inverse function for fnof; is a function in the opposite direction, from B to A , with the property that a round trip (a composition) from A to B to A (or from B to A to B ) returns each… … Wikipedia
inverse function — noun a function obtained by expressing the dependent variable of one function as the independent variable of another; f and g are inverse functions if f(x)=y and g(y)=x (Freq. 1) • Hypernyms: ↑function, ↑mathematical function, ↑single valued… … Useful english dictionary
inverse function — noun A function that does exactly the opposite of another; formally the inverse function of a function exists such that: . Halving is the inverse function of doubling … Wiktionary
inverse function — noun Date: 1816 a function that is derived from a given function by interchanging the two variables < y = ∛x is the inverse function of y = x3 > compare logarithmic function … New Collegiate Dictionary
inverse function — /ɪnvɜs ˈfʌŋkʃən/ (say invers fungkshuhn) noun the mathematical function which replaces another function when the dependent and independent variables of the first function are interchanged. If y is a trigonometrical ratio of the angle x, as y =… … Australian English dictionary
inverse function — atvirkštinė funkcija statusas T sritis fizika atitikmenys: angl. inverse function vok. inverse Funktion, f rus. обратная функция, f pranc. fonction inverse, f … Fizikos terminų žodynas
inverse function — function which is reached by expressing the dependent variable of one function as the independent variable of another (Mathematics) … English contemporary dictionary
inverse function — in′verse func′tion n. math. math. the function that replaces another function when the dependent and independent variables of the first function are interchanged for an appropriate set of values of the dependent variable • Etymology: 1810–20 … From formal English to slang
Inverse function theorem — In mathematics, specifically differential calculus, the inverse function theorem gives sufficient conditions for a function to be invertible in a neighborhood of a point in its domain. The theorem also gives a formula for the derivative of the… … Wikipedia